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This research demonstrates fuzzy outcomes using fractional integrals in q-multiplier transformations, suggesting new theoretical insights.
q-calculus and fractional calculus combined with geometric function theory lead to remarkable results. The fractional integral introduced by Riemann–Liouville applied to the q-multiplier transformation is used in this research to study the two dual theories of fuzzy differential subordination and fuzzy differential superordination and to develop specific fuzzy results. In the theorems examining fuzzy differential subordinations and fuzzy differential superordinations, fuzzy best dominants and fuzzy best subordinants are also provided. In addition, the demonstrated outcomes reveal corollaries by taking specific functions with established geometric features into consideration as the fuzzy best subordinant and fuzzy best dominant. The work concludes with a fuzzy differential sandwich theorem and related corollaries that combine the findings of this research on fuzzy differential subordinations and superordinations.
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Lupas et al. (2026) studied this question.
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